All M are N. Some N are not M. Is the set of statements consistent?

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Multiple Choice

All M are N. Some N are not M. Is the set of statements consistent?

The statements are about whether there can be a situation where both are true. “All M are N” means every element of M is also in N, so M is contained in N. “Some N are not M” says there exists at least one element that is in N but not in M. These two can hold at the same time if M is a proper subset of N (N has extra elements not in M). For example, take M = {a} and N = {a, b}. Then every M is in N, and there is an element b in N that is not in M. So both statements can be true together. Because there is a concrete model making both true, the set of statements is consistent. It is not saying M equals N, since the second statement guarantees there are N elements not in M.

The statements are about whether there can be a situation where both are true. “All M are N” means every element of M is also in N, so M is contained in N. “Some N are not M” says there exists at least one element that is in N but not in M. These two can hold at the same time if M is a proper subset of N (N has extra elements not in M).

For example, take M = {a} and N = {a, b}. Then every M is in N, and there is an element b in N that is not in M. So both statements can be true together.

Because there is a concrete model making both true, the set of statements is consistent. It is not saying M equals N, since the second statement guarantees there are N elements not in M.

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